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"cells": [
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"cell_type": "markdown",
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"source": [
"# Useful Functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Find the maximum drawdown"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`PerformanceAnalytics` provides several functions to calculate the drawdowns. What I offered here is an alternative to `PerformanceAnalytics::table.Drawdowns`. The benefits of my solutoin are:\n",
"\n",
"- It's **1.89x** faster than `table.Drawdowns`.\n",
"\n",
"- It doesn't require the user to convert the input into a `zoo` or `xts` object, which is convenient if you're using `data.table`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Create a Sample Data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The only inputs of our `drawdowns` function are 1) a return vector `ret` and 2) a date vector `date`. Note they should belong to the same stock.\n",
"\n",
"Let's generate these two variables."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
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"set.seed(42)\n",
"\n",
"# Generate 100 returns with mean 0 and standard deviation 0.05\n",
"ret = rnorm(100, mean=0, sd=0.05)\n",
"\n",
"# Generate 100 dates starting from 2010/1/1\n",
"date = seq(as.Date(\"2010/1/1\"), by=\"day\", length.out=100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The `drawdowns` Function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `drawdowns` below is a faster alternative to `PerformanceAnalytics`.\n",
"\n",
"**Inputs:**\n",
"- `ret`: a vector of returns\n",
"- `date`: a vector of dates\n",
"- `top`: the number of largest drawdowns to be returned\n",
"\n",
"**Output:**\n",
"A `data.table` with the following columns:\n",
"- `start`: the start date of the drawdown\n",
"- `trough`: the date of the trough\n",
"- `end`: the last day of the darwdown (if new watermark hasn't been reached yet, it's the last day in the sample).\n",
"- `depth`: the drawdown (percentage)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"vscode": {
"languageId": "r"
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"outputs": [
{
"data": {
"text/html": [
"<table class=\"dataframe\">\n",
"<caption>A data.table: 2 × 4</caption>\n",
"<thead>\n",
"\t<tr><th scope=col>start</th><th scope=col>trough</th><th scope=col>end</th><th scope=col>depth</th></tr>\n",
"\t<tr><th scope=col><date></th><th scope=col><date></th><th scope=col><date></th><th scope=col><dbl></th></tr>\n",
"</thead>\n",
"<tbody>\n",
"\t<tr><td>2010-01-13</td><td>2010-02-16</td><td>2010-04-10</td><td>-0.49650974</td></tr>\n",
"\t<tr><td>2010-01-02</td><td>2010-01-02</td><td>2010-01-03</td><td>-0.02823491</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"A data.table: 2 × 4\n",
"\\begin{tabular}{llll}\n",
" start & trough & end & depth\\\\\n",
" <date> & <date> & <date> & <dbl>\\\\\n",
"\\hline\n",
"\t 2010-01-13 & 2010-02-16 & 2010-04-10 & -0.49650974\\\\\n",
"\t 2010-01-02 & 2010-01-02 & 2010-01-03 & -0.02823491\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.table: 2 × 4\n",
"\n",
"| start <date> | trough <date> | end <date> | depth <dbl> |\n",
"|---|---|---|---|\n",
"| 2010-01-13 | 2010-02-16 | 2010-04-10 | -0.49650974 |\n",
"| 2010-01-02 | 2010-01-02 | 2010-01-03 | -0.02823491 |\n",
"\n"
],
"text/plain": [
" start trough end depth \n",
"1 2010-01-13 2010-02-16 2010-04-10 -0.49650974\n",
"2 2010-01-02 2010-01-02 2010-01-03 -0.02823491"
]
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"metadata": {},
"output_type": "display_data"
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"source": [
"library(data.table)\n",
"\n",
"drawdowns <- function(ret, date, top=5) {\n",
" # This function calculates the drawdowns for a given return series\n",
" # Input:\n",
" # ret: a vector of returns\n",
" # date: a vector of dates\n",
" # top: the number of largest drawdowns to be returned\n",
"\n",
" input = data.table(date, ret)[order(date)]\n",
"\n",
" # a drawdown is defined whenever the cumulative return is below the previous peak\n",
" drawdowns_raw = input[, {\n",
" ret_cum=cumprod(1 + ret)\n",
" ret_cummax=cummax(c(1, ret_cum))[-1]\n",
" drawdowns=ret_cum/ret_cummax - 1\n",
" list(date, ret, ret_cum, ret_cummax, drawdowns)\n",
" }]\n",
"\n",
" # print(drawdowns_raw)\n",
"\n",
" # find the largest drawdowns\n",
" drawdowns = drawdowns_raw[, ':='(grp = rleid(drawdowns<0))\n",
" ][drawdowns<0, \n",
" .(start=date[1], trough=date[which.min(drawdowns)],\n",
" end=date[.N], depth=drawdowns[which.min(drawdowns)]),\n",
" keyby=.(grp)\n",
" ][order(depth)]\n",
"\n",
" # return the top drawdowns\n",
" top = fifelse(top > nrow(drawdowns), nrow(drawdowns), top)\n",
" drawdowns = drawdowns[1:top][, ':='(grp=NULL)]\n",
" \n",
" return(drawdowns[])\n",
"}\n",
"\n",
"drawdowns(ret, date, top=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we use `PerformanceAnalytics::table.Drawdowns`, the code and result are offered below. As you can see, the result is the same."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"dataframe\">\n",
"<caption>A data.frame: 2 × 3</caption>\n",
"<thead>\n",
"\t<tr><th scope=col>From</th><th scope=col>Trough</th><th scope=col>Depth</th></tr>\n",
"\t<tr><th scope=col><date></th><th scope=col><date></th><th scope=col><dbl></th></tr>\n",
"</thead>\n",
"<tbody>\n",
"\t<tr><td>2010-01-13</td><td>2010-02-16</td><td>-0.4965</td></tr>\n",
"\t<tr><td>2010-01-02</td><td>2010-01-02</td><td>-0.0282</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"A data.frame: 2 × 3\n",
"\\begin{tabular}{lll}\n",
" From & Trough & Depth\\\\\n",
" <date> & <date> & <dbl>\\\\\n",
"\\hline\n",
"\t 2010-01-13 & 2010-02-16 & -0.4965\\\\\n",
"\t 2010-01-02 & 2010-01-02 & -0.0282\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 2 × 3\n",
"\n",
"| From <date> | Trough <date> | Depth <dbl> |\n",
"|---|---|---|\n",
"| 2010-01-13 | 2010-02-16 | -0.4965 |\n",
"| 2010-01-02 | 2010-01-02 | -0.0282 |\n",
"\n"
],
"text/plain": [
" From Trough Depth \n",
"1 2010-01-13 2010-02-16 -0.4965\n",
"2 2010-01-02 2010-01-02 -0.0282"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"suppressMessages({library(PerformanceAnalytics)})\n",
"\n",
"inputs = zoo(ret, order.by=date)\n",
"table.Drawdowns(inputs, top=2)[, c('From', 'Trough', 'Depth')]"
]
}
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